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Preparing for CDS Elementary Mathematics is a challenging task for the aspirants. Around 10-15 questions were asked from trigonometry section in CDS 2016. Thus, weightage of trigonometry in UPSC CDS exam is around 12-15%, according to CDS previous years’ papers. Candidates should focus more on identity type based questions rather than direct formulae based questions for scoring better in **CDS**.

Solving questions based on trigonometry ratios should be given first priority while attempting **CDS** Elementary Mathematics Paper. There are some more tips to excel the preparation for trigonometry based questions.

**Pythagoras Theorem-** You must be knowing about it. Perpendicular, Base and Hypotenuse, where Perpendicular is always opposite to the angle theta ‘Θ’.

In the above diagram, BC is the perpendicular and AC is the base of right-angled triangle ABC. Learn the order of trigonometry ratios. Here’s the secret mantra- **“Pandit Badri Prasad Har Har Bhole”** (PBPHHB)

Sin Cos Tan

__P B P__

H H B

Cosec Sec Cot

- Learn by heart the values of ratios (0
^{o}, 15^{o}, 30^{o}, 45^{o}, 60^{o}, 90^{o}) of Cosine, Sine and Tangent. - Even though trigonometric ratios have more importance, you should know the trigonometric identities as well.
- Practice by using the perpendicular side as the opposite side of angle theta.
- While solving the mathematical problems consider the symbols of trigonometric ratios carefully.
- Always read the questions carefully during the exam. Mark the questions which you find difficult and try to solve them later.
- In height and distance questions, keep in mind the form of angle (angle of elevation or angle of depression) given in the particular question.
- Practice Language based questions that will help you in Height and Distance problems.
- Your main focus should be on the identities and relations of tanθ, Cotθ, Secθ and Cosecθ.
- Practice level-III questions so that you can solve level-I and level-II easily in the examination.

Apart from the given tips for CDS 2018 preparation, it is important for you to learn some of the trigonometric identities and ratios which is given below:

- sin
^{2}θ + cos^{2}θ = 1 - tan
^{2}θ + 1 = sec^{2}θ - cot
^{2}θ + 1 = cosec^{2}θ

**Negative of a Function:**

- sin (–x) = –sin x
- cos (–x) = cos x
- tan (–x) = –tan x
- cosec (–x) = –cosec x
- sec (–x) = sec x
- cot (–x) = –cot x
- sin(x+y) = sinx cosy + cosx siny
- sin(x-y) = sinx cosy – cosx siny
- cos(x+y) = cosx cosy – sinx siny
- cos(x-y) = cosx cosy + sinx siny

**Angle of Elevation:** Let AB be a tower/pillar/shell/minar/pole) on the base BC and C is the person looking at the top of AB.

The angle ACB, made by hypotenuse AC and base BC is called the angle of elevation.

**Angle of Depression:** If observer is at Q and is viewing an object R on the ground SR, then angle between PQ and QR is the angle of depression.

**Numerically, angle of elevation is equal to the angle of depression.** In the following table, the value of ‘Θ’ is mentioned-

Angle | 0^{o} | 30^{o} | 45^{o} | 60^{o} | 90^{o} |
---|---|---|---|---|---|

Sin | 0 | ½ | 1/√2 | √3/2 | 1 |

Cos | 1 | √3/2 | 1/√2 | ½ | 0 |

Tan | 0 | 1/√3 | 1 | √3 | ∞ |

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